The invention relates to deep ultraviolet microlithography systems and to optical elements of such imaging devices, particularly those used for imaging wavelengths shorter than 200 nanometers (nm), by controlling photoelastic birefringence in cubic crystal structures of the optical elements to counteract intrinsic birefringence apparent at the shorter wavelengths.
The imaging of shorter wavelengths of light beneath the visible spectrum with cubic crystalline materials such as calcium fluoride (CaF2), barium fluoride (BaF2), and strontium fluoride (SrF2) can be detrimentally affected by details of their crystal structures that are of less consequence to longer wavelengths. Atomic details of the crystal structures, whose effects are normally subject to averaging at the longer wavelengths, can produce a pronounced birefringence at wavelengths beneath the visible spectrum.
The unwanted birefringence reduces the quality and performance of optical elements, particularly those used in optical imaging systems. Care is normally taken to avoid or reduce photoelastic birefringence resulting from unbalanced stresses acting on optical materials. Annealing is commonly used to relieve internal stresses, and mounting systems are generally designed to avoid applying external stresses. However, even if the photoelastic birefringence is entirely avoided, the intrinsic birefringence remains as a problem for optical systems employing shorter wavelengths such as those within the ultraviolet spectrum.
A paper entitled xe2x80x9cOn the Signs of the Elasto-Optic Coefficientsxe2x80x9d by Jan Smit, published by the Journal of Applied Physics 49[5], May 1978 on pages 2935-2936 provides mathematical support for understanding the use of photoelastic constants for describing the effects of stresses in a range of optical materials, and this paper is hereby incorporated by reference. A more complete treatment of the photoelastic behavior of crystalline structures is found in a text entitled Physical Properties of Crystals, by J. F. Nye, published by Clarenden Press, Oxford, 2000, particularly chapter XIII entitled xe2x80x9cNatural and Artificial Double refraction. Second-Order Effectsxe2x80x9d. The entire text as it relates to the issue of birefringence is hereby incorporated by reference. A similar treatment of silicon crystals that exhibit intrinsic birefringence in the infrared spectrum is disclosed in a paper entitled xe2x80x9cOptical Anisotropy of Silicon Single Crystalsxe2x80x9d by J. Pastrnak and K. Vedam published by Physical Review B, volume 3, number 8, pages 2567-2571, Apr. 16, 1971, which is also hereby incorporated by reference.
Our invention in one or more of its preferred embodiments compensates for the intrinsic birefringence of optical elements with cubic crystalline structures by producing counteracting photoelastic birefringence within the same or similar optical elements. Stresses applied to the optical elements in selected magnitudes and directions alter the effective crystal structures of the optical elements producing a photoelastic birefringence that combines with the intrinsic birefringence to reduce overall birefringence in directions of intended light propagation through the optical elements. Improvements in the quality and performance of the optical elements with reduced birefringence are expected.
The perturbations produced by both intrinsic birefringence and photoelastic birefringence in a crystal element can be expressed as changes to a rank two dielectric impermeability tensor Bij whose elements define an index ellipsoid sometimes referred to as an xe2x80x9cindicatrixxe2x80x9d. Intersections of the index ellipsoid with a plane normal to the direction of light propagation through the defined crystal element form an ellipse whose major and minor axes represent maximum and minimum refractive indexes and their two orthogonal directions. Differences between the lengths of the two axes are minimized to reduce birefringence in the considered direction of propagation. Optimization routines can be used to minimize overall birefringence throughout a range of directions responsible for carrying out imaging or other optical functions through the crystal element.
The changes in the dielectric impermeability tensor as a result of photoelastic birefringence can be expressed a matrix product of an array of optical constants arranged a rank four tensor qijkl and an array of stress components "sgr"kl arranged as a rank two tensor. Similarly, the changes to the dielectric impermeability tensor as a result of intrinsic birefringence can be expressed as a matrix product of an analogous rank four tensor Rijkl and components kk and kl of a nonzero photon wavevector k. The two matrix products can be added together to combine the elements of photoelastic and intrinsic birefringence. The symmetries of cubic crystals greatly simplify the combined expressions into a limited number of terms, which allow the influence of stresses to be observed on the total birefringence exhibited in selected directions of light propagation.
The stresses required to compensate for the intrinsic birefringence can be applied in the form of tensile stress, compressive stress, or shear stress. Conventional piezoelectric elements or adjustable mechanical fixturing can be used to apply the required stresses from points external to the crystal elements. Similar stresses can also be introduced by controlling thermal gradients in the crystal elements or by ion diffusion, such as practiced for making gradient index lenses.
The intrinsic birefringence can also be reduced by controlling polarization characteristics of the light propagating through the crystal elements. Although the wavelength of the propagating light may be selected for meeting certain imaging or resolution requirements, the polarization characteristics of the light can be controlled to reduce the effects of birefringence. For example, polarizations with desired orientations or symmetries (e.g., three-fold symmetry) can be used to match crystal characteristics to reduce the magnitude of intrinsic birefringence rather than counteract intrinsic birefringence with an opposite photoelastic birefringence.
The corrections made for intrinsic birefringence of a plurality of crystal elements within a common optical lithography system can be made individually within each of the crystal elements or collectively within a selected one or more but less than all of the crystal elements. A cumulative amount of birefringence exhibited by a combination of crystal elements in an optical system can be determined, and corrections can be made by producing an opposite amount of photoelastic birefringence in one of the crystal elements or in a combination of the crystal elements. The photoelastic birefringence produced in individual crystal elements does not necessarily match the intrinsic birefringence exhibited by the same crystal elements, but contributes to an amount of photoelastic birefringence that matches (or at least significantly reduces) the cumulative amount of intrinsic birefringence exhibited by the combination of crystal elements within an optical system. For example, the counteracting photoelastic birefringence produced in one of the optical elements can be sized (a) significantly larger than the intrinsic birefringence exhibited by the one optical element and (b) not significantly larger than the cumulative intrinsic birefringence exhibited by the combination of optical elements. Birefringence from other sources can be similarly corrected.